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Notes03

Notes03 - Lecture 3 Univariate and Bivariate Probability...

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1 FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007 Lecture 3 – Univariate and Bivariate Probability Agenda É Simulation of Exponential Random Variable É Simulation of Uniform Random Variable É Simulation of Gumbel Random Variable É Non-Parametric Density Models É Bivariate Continuous Distributions É Multivariate Continuous Distributions É Bivariate Discrete Distributions É Multivariate Discrete Distributions 2 FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007 Simulation of Exponential Random Variable We use the inversion of CDF transformation from Lecture 2 to generate sample random variables or deviates that are independent and identically distributed (i.i.d.) according the following exponential distribution ( ) ( ) ( ) 1 exp X F x x H x λ = We define the following relationship ( ) 1 X X F U = 3 FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007 Simulation of Exponential Random Variable ( ) ( ) ( ) ( ) 1 1 exp exp 1 log 1 log 1 U X X U X U X U λ λ λ λ = = = = − Excel workbook file Class03a.xls contains the sample simulation. R workspace contains the corresponding simulation using R. Let’s estimate the mean and variance of an exponential random variable.

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